We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in ${\mathbb{R}}^{2+1}$. We aim to establish the small data global existence result, and in addition, we also illustrate the sharp pointwise asymptotic behaviour of the solution to the coupled system. The initial data are not required to have compact support, and this is achieved by applying Alinhac's ghost weight method to both the wave and the Klein-Gordon equations.

中文翻译：

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二维零条件下波和 Klein-Gordon 系统的全局解

我们有兴趣研究具有零二次非线性的耦合波和 Klein-Gordon 方程 ${\mathbb{电阻}}^{2+1}$. 我们旨在建立小数据全局存在结果，此外，我们还说明了耦合系统解的尖锐点渐近行为。初始数据不需要有紧致支撑，这是通过将 Alinhac 的鬼权重方法应用于波浪方程和 Klein-Gordon 方程来实现的。